diff --git a/Doc/lib/libdecimal.tex b/Doc/lib/libdecimal.tex index 40c1e9103e9..7b4122a49c2 100644 --- a/Doc/lib/libdecimal.tex +++ b/Doc/lib/libdecimal.tex @@ -525,11 +525,11 @@ The \class{Context} class defines several general purpose methods as well as a large number of methods for doing arithmetic directly in a given context. \begin{methoddesc}{clear_flags}{} - Sets all of the flags to \constant{0}. + Resets all of the flags to \constant{0}. \end{methoddesc} \begin{methoddesc}{copy}{} - Returns a duplicate of the context. + Return a duplicate of the context. \end{methoddesc} \begin{methoddesc}{create_decimal}{num} @@ -1118,3 +1118,156 @@ def sin(x): return +s \end{verbatim} + + + +\subsection{Decimal FAQ \label{decimal-faq}} + + +Q. It is cumbersome to type \code{decimal.Decimal('1234.5')}. Is there a way +to minimize typing when using the interactive interpreter? + +A. Some users abbreviate the constructor to just a single letter: + +\begin{verbatim} +>>> D = decimal.Decimal +>>> D('1.23') + D('3.45') +Decimal("4.68") +\end{verbatim} + + +Q. In a fixed-point application to two decimal places, some inputs +have many places and need to be rounded. Others are not supposed to have +excess digits and need to be validated. What methods should be used? + +A. The \method{quantize()} method rounds to a fixed number of decimal places. +If the \constant{Inexact} trap is set, it is also useful for validation: + +\begin{verbatim} +>>> TWOPLACES = Decimal(10) ** -2 # same as Decimal('0.01') + +>>> # Round to two places +>>> Decimal("3.214").quantize(TWOPLACES) +Decimal("3.21") + +>>> # Validate that a number does not exceed two places +>>> Decimal("3.21").quantize(TWOPLACES, context=Context(traps=[Inexact])) +Decimal("3.21") + +>>> Decimal("3.214").quantize(TWOPLACES, context=Context(traps=[Inexact])) +Traceback (most recent call last): + ... +Inexact: Changed in rounding +\end{verbatim} + + +Q. Once I have valid two place inputs, how do I maintain that invariant +throughout an application? + +A. Some operations like addition and subtraction automatically preserve fixed +point. Others, like multiplication and division, change the number of decimal +places and need to be followed-up with a \method{quantize()} step. + + +Q. There are many ways to write express the same value. The numbers +\constant{200}, \constant{200.000}, \constant{2E2}, and \constant{.02E+4} all +have the same value at various precisions. Is there a way to transform them to +a single recognizable canonical value? + +A. The \method{normalize()} method maps all equivalent values to a single +representive: + +\begin{verbatim} +>>> values = map(Decimal, '200 200.000 2E2 .02E+4'.split()) +>>> [v.normalize() for v in values] +[Decimal("2E+2"), Decimal("2E+2"), Decimal("2E+2"), Decimal("2E+2")] +\end{verbatim} + + +Q. Is there a way to convert a regular float to a \class{Decimal}? + +A. Yes, all binary floating point numbers can be exactly expressed as a +Decimal. An exact conversion may take more precision than intuition would +suggest, so trapping \constant{Inexact} will signal a need for more precision: + +\begin{verbatim} +def floatToDecimal(f): + "Convert a floating point number to a Decimal with no loss of information" + # Transform (exactly) a float to a mantissa (0.5 <= abs(m) < 1.0) and an + # exponent. Double the mantissa until it is an integer. Use the integer + # mantissa and exponent to compute an equivalent Decimal. If this cannot + # be done exactly, then retry with more precision. + + mantissa, exponent = math.frexp(f) + while mantissa != int(mantissa): + mantissa *= 2.0 + exponent -= 1 + mantissa = int(mantissa) + oldcontext = getcontext() + setcontext(Context(traps=[Inexact])) + try: + while True: + try: + return mantissa * Decimal(2) ** exponent + except Inexact: + getcontext().prec += 1 + finally: + setcontext(oldcontext) +\end{verbatim} + + +Q. Why isn't the \function{floatToDecimal()} routine included in the module? + +A. There is some question about whether it is advisable to mix binary and +decimal floating point. Also, its use requires some care to avoid the +representation issues associated with binary floating point: + +\begin{verbatim} +>>> floatToDecimal(1.1) +Decimal("1.100000000000000088817841970012523233890533447265625") +\end{verbatim} + + +Q. Within a complex calculation, how can I make sure that I haven't gotten a +spurious result because of insufficient precision or rounding anomalies. + +A. The decimal module makes it easy to test results. A best practice is to +re-run calculations using greater precision and with various rounding modes. +Widely differing results indicate insufficient precision, rounding mode +issues, ill-conditioned inputs, or a numerically unstable algorithm. + + +Q. I noticed that context precision is applied to the results of operations +but not to the inputs. Is there anything to watch out for when mixing +values of different precisions? + +A. Yes. The principle is that all values are considered to be exact and so +is the arithmetic on those values. Only the results are rounded. The +advantage for inputs is that ``what you type is what you get''. A +disadvantage is that the results can look odd if you forget that the inputs +haven't been rounded: + +\begin{verbatim} +>>> getcontext().prec = 3 +>>> Decimal('3.104') + D('2.104') +Decimal("5.21") +>>> Decimal('3.104') + D('0.000') + D('2.104') +Decimal("5.20") +\end{verbatim} + +The solution is either to increase precision or to force rounding of inputs +using the unary plus operation: + +\begin{verbatim} +>>> getcontext().prec = 3 +>>> +Decimal('1.23456789') # unary plus triggers rounding +Decimal("1.23") +\end{verbatim} + +Alternatively, inputs can be rounded upon creation using the +\method{Context.create_decimal()} method: + +\begin{verbatim} +>>> Context(prec=5, rounding=ROUND_DOWN).create_decimal('1.2345678') +Decimal("1.2345") +\end{verbatim}